PS-hollow representations of modules over commutative rings

Let [Formula: see text] be a commutative ring and [Formula: see text] a nonzero [Formula: see text]-module. We introduce the class of pseudo-strongly[Formula: see text]PS[Formula: see text]-hollow submodules of [Formula: see text]. Inspired by the theory of modules with secondary representations, we investigate modules which can be written as finite sums of PS-hollow submodules. In particular, we provide existence and uniqueness theorems for the existence of minimal PS-hollow strongly representations of modules over Artinian rings.

NONLINEAR SINGULAR STURM-LIOUVILLE PROBLEMS WITH IMPULSIVE CONDITIONS

In this paper, we consider a non-linear impulsive Sturm-Liouville problem on semiinfinite intervals in which the limit-circle case holds at infinity for THE Sturm-Liouville expression. We prove the existence and uniqueness theorems for this problem.

Best Proximity Point Results for Geraghty Type Ƶ-Proximal Contractions with an Application

In this study, we establish the existence and uniqueness theorems of the best proximity points for Geraghty type Ƶ-proximal contractions defined on a complete metric space. The presented results improve and generalize some recent results in the literature. An example, as well as an application to a variational inequality problem are also given in order to illustrate the effectiveness of our generalizations.